Question: What do the following two equations represent? $-2x+3y = 2$ $-3x-2y = 3$
Answer: Putting the first equation in $y = mx + b$ form gives: $-2x+3y = 2$ $3y = 2x+2$ $y = \dfrac{2}{3}x + \dfrac{2}{3}$ Putting the second equation in $y = mx + b$ form gives: $-3x-2y = 3$ $-2y = 3x+3$ $y = -\dfrac{3}{2}x - \dfrac{3}{2}$ The slopes are negative inverses of each other, so the lines are perpendicular.